Methodological study on diffusion tensor indices in MS: analysis challenges and outcomes

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UNIVERSIDADE DE LISBOA FACULDADE DE CIˆENCIAS

DEPARTAMENTO DE F´ISICA

Methodological Study on Diffusion Tensor

Indices in MS: Analysis Challenges and

Outcomes

Catarina Correia de Freitas

Disserta¸c˜ao

Mestrado Integrado em Engenharia Biomédica e Biof´ısica Perfil de Radia¸cões em Diagnóstico e Terapia

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UNIVERSIDADE DE LISBOA FACULDADE DE CIˆENCIAS

DEPARTAMENTO DE F´ISICA

Methodological Study on Diffusion Tensor

Indices in MS: Analysis Challenges and

Outcomes

Catarina Correia de Freitas

Disserta¸c˜ao

Mestrado Integrado em Engenharia Biomédica e Biof´ısica Perfil de Radia¸cões em Diagnóstico e Terapia

Orientador externo: Professora Doutora Claudia Wheeler-Kingshott Orientador interno: Professora Doutora Rita G. Nunes

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Resumo

A imagem de tensor de difusão (ITD) é uma modalidade de ressonância magnética (RM) que permite determinar in vivo a intensidade e a dire¸cão da di-fusão da água nos tecidos biológicos. A mobilidade molecular nos tecidos depende da sua organiza¸cão celular. Em estruturas organizadas, como na substância branca do cérebro, em que há uma grande compacta¸cão de fibras nervosas, a difusão é restringida na direçcão perpendicular aos axónios e ocorre preferencialmente na dire¸cão paralela às fibras. Como esta direcionalidade é observável com a ITD, esta técnica permite concluir acerca da microestrutura dos tecidos e investigar altera¸cões estruturais que ocorrem em caso de patologia. O fato de a ITD proporcionar novos contrastes da estrutura da substância branca comparativamente à imagem de RM convencional, torna-a uma técnica apelativa para inúmeros estudos neurológicos, designadamente, estudos de doen¸cas neurodegenerativas, como a esclerose múltipla (EM).

Na ITD, a difusão em cada voxel é descrita por um tensor que, após diagonal-izado, pode ser definido por três valores próprios, λ1, λ2 e λ3 e os seus

correspon-dentes vetores próprios, v1, v2 e v3. Através desta informa¸cão, o tensor de difusão

(TD) pode ser representado geometricamente como um elipsóide cujos eixos estão alinhados com os vetores próprios e cujas dimensões estao de acordo com a raiz quadrada dos valores próprios. Por sua vez, o maior eixo do elipsóide corresponde `

a dire¸cão principal da difusão, que se assume como sendo paralela à dire¸cão das fibras nervosas.

A informa¸cão dada pelos tensores pode ser mais facilmente visualizada calcu-lando ´ındices que correspondem a certas propriedades da difusão. Nomeadamente, o primeiro valor próprio define o parâmetro de difusibilidade axial (DA), o qual está associado à difusão na dire¸cão das fibras nervosas, e a média do segundo e terceiro valores próprios corresponde ao parâmetro de difusibilidade radial (DR), o qual mede a difusão na dire¸cão perpendicular às fibras. Altera¸cões nestes dois parâmetros são associadas, respetivamente, à degenera¸cão axonal e à desmielin-iza¸cão dos neurónios. Outros ´ındices são a difusibilidade média (DM), que corre-sponde à média dos três valores próprios, e a anisotropia fracional (AF), que mede a direcionalidade da difusão, a qual pode variar entre 0 (isotrópica) e 1 (extremamente direcionada).

No entanto, existem algumas limita¸cões associadas à IDT que dificultam a inter-preta¸cão dos seus resultados. Em primeiro lugar, o modelo que é utilizado é incapaz

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de representar voxeis onde ocorre cruzamento de tratos não paralelos de fibras ner-vosas. Nos restantes casos, fatores como uma baixa razão sinal-ru´ıdo e a presen¸ca de lesões podem desviar o tensor da dire¸cão correta das fibras nervosas. Nestes casos, a compara¸cão de ´ındices de difusão entre diferentes sujeitos pode resultar em conclusões enganadoras, dado que se estão a comparar valores que correspondem `

as caracter´ısticas da difus˜ao ao longo de diferentes estruturas biol´ogicas.

Este projeto teve como objetivo criar e testar uma metodologia, com base no tra-balho desenvolvido por Wheeler-Kingshott et al. (2012), para comparar, de forma consistente, a informa¸cão dada pelas imagens de TD entre um grupo de indiv´ıduos saudáveis e um grupo de pacientes com EM. Neste método, em cada voxel, os ´ındices de difusão não são calculados diretamente a partir dos valores próprios do TD, mas da proje¸cão dos TD na dire¸cão de vetores próprios de referência, que se assumem como estando alinhados com a dire¸cão saudável das fibras nervosas. Estes vetores próprios são retirados de uma imagem de TD de referência constru´ıda a partir da média de imagens de TD correspondentes aos sujeitos saudáveis da popula¸cão. No estudo desenvolvido, participaram 48 controlos e 76 doentes com EM.

Para se poder comparar as diferen¸cas entre o grupo de pacientes e o grupo de indiv´ıduos saudáveis, foi primeiro necessário proceder à normaliza¸cão das imagens de TD. Assim, estas imagens foram alinhadas a um template criado a partir de um subconjunto de 20 controlos e 20 pacientes. Para o alinhamento, foram utilizados dois métodos diferentes: um baseado nas próprias imagens de DT e o outro baseado nos mapas escalares de AF dessas imagens e do template.

De seguida, foram obtidos os vetores e os valores principais de cada tensor das imagens da popula¸cão em estudo. Com estes valores principais, foram calculados os ´ındices DA, DR e AF. Foram igualmente calculados os pares de vetores e valores principais para a imagem de referência. Os tensores de cada sujeito foram pro-jetados nas dire¸cões de referência, dando origem aos valores principais projetados. Estes últimos foram utilizados para calcular os ´ındices projetados: difusibilidade ax-ial projetada (DAP), difusibilidade radax-ial projetada (DRP) e anisotropia fracional projetada (AFP).

Para cada método de alinhamento utilizado, foi conduzida uma análise es-tat´ıstica para comparar as diferen¸cas detectadas entre o grupo de controlos e o grupo de pacientes usando os ´ındices normais e os ´ındices projectados. Os resulta-dos mostraram que existiu um aumento de DA, DR, DAP e DRP e uma diminui¸cão de AF e AFP nos pacientes em rela¸cão aos controlos. A extensão e a localiza¸cão das altera¸cões entre parâmetros análogos (DA e DAP, DR e DRP, e AF e AFP) foram detetadas de forma muito semelhante, sobrepondo-se em grande parte e diferindo apenas em algumas pequenas zonas. Foram observadas diferen¸cas mais extensas

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entre os parâmetros projetados e os parâmetros normais através do método de alinhamento que utilizava os mapas de AF. Contudo, apesar de não terem sido observados resultados conclusivos, foram identificadas algumas diferen¸cas que po-dem sugerir uma maior sensibilidade dos parametros projetados para identificar os elementos patológios da EM.

As altera¸cões detetadas com os parâmetros normais derivados de ambas as técnicas de alinhamento foram também comparadas, o que mostrou que os resul-tados podem ser consideravelmente influenciados pela técnica (baseada nos mapas AF ou nas imagens de TD) escolhida para o alinhamento das imagens. Foi também observado que o alinhamento com as imagens de AF é menos eficaz a alinhar os tensores com o template. De fato, verificou-se uma maior dispersão na orienta¸cão dos tensores do grupo em estudo utilizando esta técnica. No entanto, é neces-sario investigar qual dos métodos de normaliza¸cão das imagens de TD é o indicado para efetuar análises comparativas entre pacientes e controlos porque, apesar de o método de TD ser mais eficaz no alinhamento dos tensores, esta reorienta¸cão pode porventura cancelar também informa¸cões adicionais sobre patologia.

Estudos postmortem deverão ser efetuados de forma a testar o fundamento biológico dos parâmetros projetados comparativamente aos parâmetros normais e também para se investigar qual dos métodos de alinhamento tem maior especifici-dade e sensibiliespecifici-dade para detetar patologia em estudos comparativos de ITD entre pacientes e controlos.

PALAVRAS-CHAVE: imagem de tensor de difusão, difusibilidade axial projetada, difusibilidade radial projetada, anisotropia fracional projetada, esclerose múltipla, alinhamento com tensor de difusão, alinhamento com anisotropia fracional.

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Abstract

Diffusion tensor imaging (DTI) characterizes the diffusion properties of the tissues through a tensor. This tensor can be used to calculate scalar indices that are used to study white matter (WM) changes in several neurological diseases. The diffusion tensor (DT) assigns a principal direction for diffusion that, in the WM of the brain, is assumed to be aligned with the direction of the axonal fibres. However, there are some cases where this supposition fails. As a result, misinterpretation of differences in DT indices between patients and healthy controls (HCs) may occur when the geometrical properties of the datasets are not taken into consideration. To solve this problem, a new analysis method consistent between subjects was introduced. Here, diffusion is measured along reference vectors that define the most probable direction of healthy diffusion. This study aimed to develop a pipeline for the use of this new approach in group comparisons of HCs and patients with multiple sclerosis (MS), and test its sensitivity at identifying pathology compared to the standard approach. This analysis was done using two different registration methods: DT-based and FA-DT-based. In general, it was shown that at a group level there were no major differences between the standard and the projected indices. However, results were observed that could suggest increased sensitivity for the latter. In addition, a significant effect of the registration method was detected in the results. Also, the coherence of tensor’s orientation between datasets was studied, which showed that the FA-based registration aligns tensors to a lesser degree than the DT-based. The pipeline developed in this work should be further investigated to enable a final conclusion regarding its validity and sensitivity. Also, additional work should be performed to investigate whether the realignment based on the DTI rather than FA properties may mask pathological processes or viceversa.

KEYWORDS: diffusion tensor imaging, projected axial diffusivity, projected radial diffusivity, projected fractional anisotropy, multiple sclerosis, DT-based registration, FA-based registration.

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Acknowledgements

The completion of this dissertation wouldn’t have been possible without the support of several people, to whom I would like to express my sincere gratitude.

First of all, I am extremely grateful to my external supervisor Dr. Claudia Wheeler-Kingshott for her help, encouragement and kindness. It as a great oppor-tunity to have worked in IoN, moreover, under her guidance, and to have learned so much with her expertise.

I would like to express my sincere gratitude to my internal supervisor Dr. Rita Nunes, who was always very supportive and helpful. In addition, I am very thankful to both my supervisors for all their patience, critics and comments when correcting my thesis.

I would also like to show my appreciation to the researchers and collaborators in IoN for the friendly work atmosphere. In particular, I thank Dr. Gary Zhang for his kind availability to help and give suggestions to my work.

I gratefully acknowledge the financial support given by the Erasmus Grant and the NMR Research Unit of UCL Institute of Neurology.

In addition, I must thank the ”Portuguese Gang” in London for all the com-panionship, dinner parties and good times. Besides them being great people, it was also very good to have a little bit of home during my stay.

I am also very much indebted to my closest friends for their support and en-couragement in the moments where I needed the most.

E por fim, gostaria de agradecer à minha fam´ılia por todo o apoio que me deram ao longo da minha vida. Agrade¸co especialmente a dedica¸cão dos meus pais, sem a qual não teria sido poss´ıvel fazer este trabalho. Agrade¸co também à minha irmã e aos meus sobrinhos por todo o carinho, palha¸cadas e alegria, que foram muito importantes para não perder a motiva¸cão durante a escrita da tese.

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List of Figures

2.1 Diffusion anisotropy in white matter . . . 4

2.2 Schematic of the pulsed field gradient spin-echo Magnetic Resonance (MR) technique introduced by Stejskal and Tanner . . . 5

2.3 Diffusion tensor ellipsoid and its dependence on the structure of phys-ical obstructions . . . 7

2.4 Visualization of the scalar indices Mean Diffusivity (MD) and Frac-tional Anisotropy (FA) . . . 8

3.1 Importance of tensor reorientation after registration . . . 18

3.2 Template . . . 20

3.3 Schematics of the projected indices calculation . . . 22

3.4 Lesion probability map . . . 24

3.5 Results showing areas with increased PAD in MS patients . . . 25

3.6 Results showing areas with increased PRD in MS patients . . . 26

3.7 Results showing areas with decreased PFA in MS patients . . . 26

3.8 Results of the comparison between the projected and original indices 27 3.9 Results of the angle dispersion analysis between the mean DT-datasets 29 4.1 Results of the comparison between the FA-based and DT-based reg-istration method . . . 36

4.2 Results of the comparison between the projected and original indices obtained with FA-based registration . . . 37

4.3 Results of the angle dispersion analysis between the mean DT-datasets obtained with FA-based registration . . . 38

4.4 Results of the angle dispersion analysis between the mean HC DT-datasets obtained with DT-based pipeline and with FA-based pipeline 39 4.5 Angle analysis histogram . . . 39

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List of Tables

2.1 Clinical meaning of each Expanded Disability Status Scale (EDSS)

score for a patient. . . 10

3.1 Subject group descriptives (mean±standard deviation). . . 15

3.2 Template group descriptives (mean±standard deviation) . . . 19

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List of Abbreviations

AD Axial Diffusivity

ADC Apparent Diffusion Coefficient BET Brain Extraction Tool

CNS Central Nervous System DD Disease Duration

DT Diffusion Tensor

DTI Diffusion Tensor Imaging DW Diffusion-Weighted

DWI Diffusion-Weighted Imaging EDSS Expanded Disability Status Scale FA Fractional Anisotropy

HCs Healthy Controls

LPM Lesion Probability Map MD Mean Diffusivity

MR Magnetic Resonance

MRI Magnetic Resonance Imaging MS Multiple Sclerosis

NAGM Normal-Appearing Gray Matter

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NAWM Normal-Appearing White Matter PAD Projected Axial Diffusivity

PFA Projected Fractional Anisotropy PP Primary Progressive

PPD Preservation of Principal Directions PR Progressive-Relapsing

PRD Projected Radial Diffusivity RD Radial Diffusivity

RF Radio-Frequency ROI Region of Interest RR Relapsing-Remitting SNR Signal-to-Noise Ratio SP Secondary Progressive SPD Symmetric Positive-Definite TE Echo Time TR Repetition Time

VBA Voxel-Based Analysis WM White Matter

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Chapter 1 Introduction

1.1 Aim of the work

Diffusion Tensor Imaging (DTI) is an Magnetic Resonance Imaging (MRI) modality that has emerged as an important new technique for characterizing White Matter (WM) microstructure in health and disease. Since damage in the tissue can affect water diffusion, this technique is able to provide in vivo information about the responsible pathological processes. Additionally, in neurodegenerative diseases as Multiple Sclerosis (MS), DTI can present a higher sensitivity and specificity at detecting abnormal regions in brain white matter compared to conventional MRI.

In DTI, each voxel is defined by a tensor aligned with the main direction of diffusion, which is assumed to be parallel to the axonal fibres. From the tensors, scalar parameters that describe the magnitude and orientation of diffusion can be calculated. When compared between patients and controls, these parameters allow to spatially localize group differences, like alterations in myelin sheath or in cell membrane integrity.

However, misinterpretation of these changes may occur when the alignment of the tensors with the underlying tissue structure is not verified. Factors like a low Signal-to-Noise Ratio (SNR) and the presence of pathology can affect the calculation of the principle direction of diffusivity, deviating the tensor from the true direction of the fibre bundle. In these cases, a comparison between DTI indices of different subjects is not coherent because the tensors represent properties of diffusion along distinct structures.

To solve this problem, a new method for performing DTI quantitative analysis was introduced, which measures diffusion along reference directions derived from Healthy Controls (HCs) [1].

This work aimed to develop and validate a pipeline for this new approach and to assess whether it can be more informative than the standard one at identifying

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CHAPTER 1. INTRODUCTION

brain WM changes in a group comparison of controls and MS patients.

In order to achieve this, this project considered two different methods of prepar-ing data for the analysis and hence this dissertation is divided into two parts.

In addition, the overall purpose of this research is to contribute to an accurate assessment of MS microstructural changes. This, in turn, will lead to an improved monitoring of the patients, in a better prediction of the course of the disease, and in the development of new treatments and therapies.

1.2 Dissertation outline

The rest of this dissertation is organized as follows. In the next chapter, important notions regarding this work are addressed, including the concepts of DTI, a brief introduction to MS pathology and a review of imaging analyses on MS. Chapter 3 describes the methodology followed in the first part of this work, shows the results obtained and presents the developed discussion and conclusions. In Chapter 4, the methods, results, discussion and conclusions of the second part of this study are detailed. Finally, Chapter 5 summarizes the results and final conclusions of this research and presents suggestions for future work.

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Chapter 2 Background

2.1 Measuring diffusion in the brain

Diffusion

Diffusion is a mass transport process that results from the thermally driven random motion of particles in a fluid, called Brownian motion [2]. At a temperature of absolute zero (0 K) there is no diffusion, however, as the temperature increases, the molecules start vibrating and colliding with each other, which leads to their translational movement [3].

The mean-squared displacement (< x2 >) of a diffusing particle over a certain time interval (∆t) depends on a physical constant called diffusion coefficient (D). The equation that describes this relationship (considering the case of free diffusion) was derived by Einstein and is presented below:

< x2 >= 2D∆t (2.1)

The diffusion coefficient is affected by the molecular weight of the particles and by the viscosity and temperature of the media [2, 4].

When there are no barriers to diffusion or in a medium where the restrictions are not geometrically coherent, the molecular mobility is identical in all directions and is called isotropic diffusion. However, if diffusion depends on direction, like in a medium with highly oriented obstructions, it is termed anisotropic.

Diffusion in the brain

In the biological tissues, water mobility is conditioned by the underlying tissue microstructure: by the size, shape and composition of any physical barriers; by the spacing between these hindrances; and also by the permeability of the cellular membrane [5, 6].

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CHAPTER 2. BACKGROUND

In the WM of the brain, which has a very organized microstructure due to the dense packing of the axonal fibres, diffusion is anisotropic. Water is free to diffuse along the direction of the neuronal fibres, both intra and extra-cellularly, but in the perpendicular direction, diffusion is restricted by the cellular membrane and the myelin sheath of the axons (Figure 2.1) [7].

Figure 2.1: Diffusion anisotropy in white matter. Both in the intra-axonal and in the interstitial spaces there is greater hindrance to the molecular displacement along the perpendicular direction (D⊥) of the fibres than along the parallel direction (Dk). Image

adapted from [8].

However, conditions such as trauma, pathology and ageing, can destruct or dis-arrange the axonal organization, causing a reduction in the anisotropy of diffusion. Therefore, by studying the diffusivity properties of the neural tissue it is possible to gain insight into the complex structural organization of brain WM and to study the changes that occur due to natural or pathologic physiological processes.

MRI sensitized to diffusion

MRI is based upon the interaction between an applied magnetic field and nuclei that possess spin. In clinical MR imaging, the most used nuclei is the hydrogen.

When exposed to an external magnetic field (B0), the spinning nuclei start to precess with a frequency proportional to the strength of the applied field, according to the Larmor equation:

ω = γB0 (2.2)

where (ω) is the precessional frequency of the spins (also called Larmor fre-quency) and γ is the proton gyromagnetic ratio, which is a constant for every atom at a particular magnetic field strength.

In conventional MRI, a homogeneous B0 is used. However, to sensitize the MR signal to diffusion, diffusion-weighting gradient pulses need to be introduced in the

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MR acquisition sequences. The MRI modality that employs this technique is called Diffusion-Weighted Imaging (DWI).

When a gradient pulse is added, it linearly alters the strength of the B0 field along the applied gradient axis. Accordingly with the Larmor equation, this change will also affect the precessional frequency of the spins [9].

Applying a linear inhomogeneity in the magnetic field makes the spins resonate at different frequencies, depending on the strength of the magnetic field by which they are being affected. At the end of the gradient application, the protons will go back to resonating at the same frequency associated with the B0 field. However, the same doesn’t happen to their phases, which is no longer identical (spins with slightly higher Larmor frequency will accumulate a greater phase). Provided the protons do not move, this dephasing can be reversed by the application of a second gradient, with opposite polarity and with the same strength and length of the first [9].

Yet, this does not happen in the presence of water motion, because the move-ment of protons between the two gradient pulses leads to imperfect rephasing, and consequently, to signal loss. In this way, the MR image is sensitized to diffusion along the axis of the applied gradients [9].

The image acquisition is generally performed using the Stejskal–Tanner sequence module illustrated in Figure 2.2 [4]. In this scheme, the gradients are applied in the form of rectangular pulses that are inserted in the dephasing and rephasing parts of the spin-echo module. Motion along the gradient axis results in a signal loss proportional to the displacement [10].

Figure 2.2: Schematic of the pulsed field gradient spin-echo MR technique introduced by Stejskal and Tanner. G and δ correspond to the magnitude and width of the diffusion gradients, respectively; and ∆ to the time interval between corresponding points of the two diffusion gradient pulses. Image adapted from [11].

Using this echo scheme, the decreased signal (S) can be compared with the original signal (S0), using the following equation, that assumes Gaussian diffusion:

S = S0e −γ2_G2_δ2 ∆− δ 3 ADC (2.3)

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Where the Apparent Diffusion Coefficient (ADC) parameter measures the mag-nitude of diffusion; γ corresponds to the proton gyromagnetic ratio; G and δ to the magnitude and width of the diffusion gradients, respectively; and ∆ to the time interval between corresponding points of the two diffusion gradient pulses [12]. By solving this equation, an ADC map can be obtained where the intensity of each voxel is proportional to the rate of water mobility in that voxel.

Moreover, this expression can be simplified using the b value, which characterizes the strength of the applied diffusion-weighting:

b = γ2G2δ2 ∆ − δ 3 (2.4) However, the use of a scalar (ADC) fails to describe the properties of ordered tissues, such as brain WM and skeletal muscle, where diffusion is anisotropic. In these cases, the ADC maps vary according to the direction of the applied magnetic field gradient.

For this reason, the DWI modality is only used to describe diffusion in isotropic media, where the rate of water mobility is identical in all directions.

In anisotropic media, diffusion needs to be characterized three-dimensionally. This is done using DTI, which uses a tensor to represent the anisotropic nature of diffusion.

2.2 Diffusion tensor imaging

DT model

In DTI, diffusion is characterized by a tensor (D) instead of a single scalar. The Diffusion Tensor (DT) is a a 3x3 Symmetric Positive-Definite (SPD) matrix. Its diagonal elements describe the molecular mobility along the three orthogonal axes of the scanner measurement frame whereas the off-diagonal elements correspond to the correlation between displacements along these axes [11]. The DT is presented below: D =    Dxx Dxy Dxz Dxy Dyy Dyz Dxz Dyz Dzz

  

Using the DT model, Eq. 2.3 is replaced by the following expression [12]: Sk = S0e−bg

T

kDgk _(2.5)

Where k varies from 1 to n, and n is the number of applied gradients; Sk is the

signal intensity measured after the application of the kthgradient in the gkdirection;

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and S0 is the original image intensity, measured with no diffusion gradients. The

product gT_k D g_k represents the diffusivity along the direction g_k.

Eq. 2.5 corresponds to a system of equations that is solved for D, the diffusion tensor. Since it has 6 independent elements, it is necessary to have at least 7 images to estimate it: 6 Diffusion-Weighted (DW) images acquired with gradients applied in 6 linearly independent directions (giving values for S1,...,S6) plus one image with

no diffusion-weighting (giving the value for S0). Typically, a much greater number

of images is acquired and then a multivariate linear regression is used to fit a tensor to the data.

In DT analysis, the tensor is diagonalized, yielding three pairs of orthogonal eigenvectors (v1, v2, and v3) and positive eigenvalues (λ1, λ2, and λ3). The

eigen-vectors are associated with the principal axes of diffusion, whereas the eigenvalues correspond to the diffusion coefficients along the corresponding axis. Additionally, the eigenvectors are sorted according to the descending order of their eigenvalues, so that, at each voxel, the eigenvector correspondent to the largest eigenvalue rep-resents the principal direction of diffusion [13].

Using the eigenvectors and the eigenvalues, the DT can be visually represented by a diffusion displacement-probability ellipsoid (Figure 2.3-A). The ellipsoid repre-sents the distance that a molecule will diffuse from the origin, with equal probability for all the possible directions. The principal axes of the ellipsoid are given by the eigenvectors, and the lengths are scaled according to the square roots of the corre-sponding eigenvalues [11].

The ellipsoid shape reflects the anisotropy of diffusion. This can be observed in Figure 2.3-B,C.

Figure 2.3: Diffusion tensor ellipsoid and its dependence on the structure of physical obstructions. A - Diffusion tensor ellipsoid. B – In an isotropic tissue, the ellipsoid is spherical. C – In coherently organized tissues, diffusion is anisotropic. Image adapted from [14].

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DTI scalar indices

The DT eigenvalues can be combined to define several quantitative scalar indices that characterize diffusion magnitude and anisotropy. The simplest scalar that measures the diffusion magnitude is the average of the tensor’s eigenvalues [15]. This average is referred to as Mean Diffusivity (MD), which corresponds to the total amount of diffusion in a voxel:

M D = λ1+ λ2+ λ3

3 (2.6)

The anisotropy measures are used to quantify the shape of the diffusion, and con-sequently, to describe the amount of tissue organization [15]. The most widely used anisotropy measure is the Fractional Anisotropy (FA):

F A = √1 2 p(λ1− λ2)2+ (λ2− λ3)2+ (λ1− λ3)2 pλ2 1+ λ22+ λ23 (2.7)

This index is scaled from 0 (isotropic diffusion) to 1 (highly directional diffusion) and is often considered a measure of white matter integrity.

Other diffusion measures are the Axial Diffusivity (AD) and the Radial Diffusiv-ity (RD). The AD, also called parallel diffusivDiffusiv-ity, is equal to the largest eigenvalue (λ1). The RD, also called perpendicular diffusivity, equals the average of the two

smaller eigenvalues (λ2 and λ3). These measures are interpreted as the diffusivity

parallel to and perpendicular to the fibre tracts [15].

Figure 2.4: Visualization of the scalar indices MD and FA. A – MD map; B – FA map; C – FA image with color coding according to the principal direction of diffusion: in this image, red corresponds to diffusion along the inferior-superior axis; blue to diffusion along the transverse axis; and green to diffusion along the anterior-posterior axis. Image adapted from [16].

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These scalar indices can be used for visualizing the diffusion tensor data. In Figure 2.4, MD (A) and FA (B) maps are exemplified. In addition, it is possible to use color coding in the FA maps according to the principal direction of diffusion, as is illustrated in Figure 2.4-C.

The DTI indices can be used probe the integrity of the brain white matter. MD, FA, AD and RD are all very popular indices not only because of their straight forward interpretation in terms of tissue characteristics, but also because they are rotationally invariant, which means that they reflect tissue geometrical properties independently of the relative position of the tissue in the scanner frame of reference and the diffusion weighting directions chosen.

Applications

DTI has been extensively used in neurological studies to quantify the changes of several brain conditions, including white matter diseases, neurophychiatric condi-tions, neurodevelopment and aging [17]. These studies are usually conducted by statistically comparing the DTI indices between two or more groups of subjects. This allows to identify what are the diffusion properties that distinguish the differ-ent groups which, in turn, can be used to investigate the biological substrate for these differences.

In addition, other important application of DTI is the three-dimentional recon-struction of the white matter tracts, which can be used to represent and measure the structural connectivity in human brains.

Limitations

Despite the promise of this imaging method, the clinical utility of DTI is limited by some factors, such as its dependency on noise and on the inaccurate assumption that water molecules obey Gaussian diffusion in biological tissues [18]. However, the major limitation of DTI is that independently of the tissue architecture, the diffusion properties of each voxel are always averaged by a single diffusion ellipsoid. Therefore, the DT model fails to describe the information of voxels that contain multiple fibres with different orientations.

2.3 Multiple sclerosis and DTI

Multiple sclerosis is a disease in which the immune system attacks the Central Nervous System (CNS), causing the demyelination and sometimes damage of the nervous fibres.

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The myelin is an electrically insulating fatty substance that surrounds the nerve fibres and serves the purpose of quickly and efficiently conducting the nervous’ impulses along the axons.

When myelin or nerve fibre damage occurs, the electrical signals transmitted throughout the brain and spinal cord are disrupted or distorted. As a consequence, the clinical symptoms of the disease can include loss of motor, cognitive, sensory and visual functions, depending on which nerves are affected [19].

The clinical condition of MS patients is classified according to the Expanded Disability Status Scale (EDSS) score. This is a standard rating system that varies from 0 to 10, quantifying the neurological impairment of MS patients. The clinical meaning of the rating system is described in Table 2.1 [20].

Table 2.1: Clinical meaning of each EDSS score for a patient. EDSS score Neurological impairment

0.0 Normal neurological examination

1.0 No disability

2.0 Minimal disability

3.0 Moderate disability

4.0 Relatively severe disability 5.0 Disability prevent full daily activities

6.0 Assistance required to walk

7.0 Restricted to a wheelchair

8.0 Restricted to a bed or chair

9.0 Confined to bed

10.0 Death

The primary cause of the disease is unknown, but it is thought to be triggered by genetic and environmental factors. Although currently there is no known cure for MS, medication exists to improve the patient’s quality of life by managing the symptoms and controlling the disease course [19].

The manifestation of MS greatly varies from patient to patient. However, there are four major different disease courses that can be distinguished: Relapsing-Remitting (RR); Secondary Progressive (SP); Primary Progressive (PP); and Progressive-Relapsing (PR)) MS [19].

The RR course is the most common MS clinical pattern (about 85% of patients are diagnosed with this type of MS). It is marked by worsening intervals of the neurologic function (relapses) and by intervals of recovery (remissions), in which there is no disease progression. The remitting periods of the disease are a result of axonal and myelin regeneration or resolution of inflammation. The SP type of

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MS occurs as an evolution of RR MS (approximately 85% of the RR MS cases evolve to the SP pattern) and is characterized by a steady progress of the disease. Finally, both PP and PR courses are distinguished by a progressive worsening of the condition from the beginning, however, in the latter, punctual attacks of worsening neurologic function occur over time [19, 21].

There is no ultimate diagnostic tool for MS. The disease is diagnosed based on the analysis of the clinical symptoms and medical history of the patient along with results from tests that include an MRI of the brain and spinal cord. Due to being a non-invasive technique and to its sensitivity for identifying demyelinating lesions, MRI is the preferred imaging method to help diagnosing MS, to monitor the course of the disease and to control the response to treatment effects [18, 19, 22].

However, conventional MRI is also limited by low sensitivity to damage in areas of Normal-Appearing White Matter (NAWM) and Normal-Appearing Gray Matter (NAGM) [18] and low pathological specificity to the heterogeneous features of MS pathology [23], which include, for example, the presence and extension of edema, demyelination, axonal injury, and remyelination [18, 23]. In addition, this lack of specificity contributes to another limitation of MRI, which is the poor association of the MRI results with the patient’s clinical manifestation of the disease [18, 23].

Other quantitative MR-based techniques, like diffusion tensor MRI, have the potential to overcome such limitations and contribute to explain the mechanisms that underlie MS pathology.

The different pathologic elements of MS can alter the permeability or geometry of the structural barriers to water diffusion in the brain, which can be depicted by DTI. In general, MS patients have an increased amount of water diffusion and a decreased anisotropy in the region of the lesions, in the surrounding lesion tissue, in the NAWM and in the NAGM. Moreover, these changes seem to be dependent on the clinical course of the patient, since they are found to be greater in patients presenting a more severe course of the disease than in less severe courses [24].

Additionally, in a mice study by Song et al., axonal damage was linked with a decrease in AD, and demyelination with a increase in RD [25,26]. Since then, a lot of studies have focused on analysing these two parameters as potential differentiators between myelin loss and axonal injury. However, although RD, FA and MD have been shown to be strong predictors of myelin content in postmortem human brain, the interpretation of changes in AD remain controversial since both increases and decreases have been reported [27].

It is clear that advances in MRI have been essential for a better understanding of the pathophysiology and clinical management of MS patients. Nevertheless, the improvement of advanced diffusion MR imaging techniques is still necessary

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in order to gain a better understanding of the disease and to improve the value of MR imaging in MS clinical assessment, especially with respect to its potential prognostic value [28].

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Chapter 3 Projected DTI indices as new

measures to study WM integrity

3.1 Motivation and objectives

DTI indices have been used in several white matter studies in attempt to qualify and quantify structural changes in the tissues. However, in order to take meaningful and accurate conclusions from this type of studies it is necessary to consider the limitations of DTI technology.

DT-MRI data is analysed based on the assumption that the principal eigenvec-tor of the DT is aligned with the direction of the white matter tracts. However, this supposition is not always valid, as in the case of voxels containing crossing fibres. Furthermore, besides this intrinsic limitation of the DT model, there are other issues that deviate the DT from the axonal bundles’ genuine direction: a low SNR of the DW-images, and the presence of lesions. In these voxels, the terminology of axial and radial diffusivities becomes no longer adequate to represent, respectively, the molecular mobility along and across the WM tracts, because the DT eigenvectors are oriented along other biological structures. Not considering the geometrical features of the tensor ellipsoid can, in this way, result in misleading conclusions when com-paring diffusion properties between group populations, especially, between healthy subjects and patients. In order to prevent deceptive interpretations of the tissue’s biophysical changes, the alignment of the DT principal direction should be checked with the underlying tissue structure geometry.

This problem was explored by Wheeler-Kingshott et al. [1, 29], who suggested a novel methodology to quantify diffusion based on projected diffusivities [1]. Two new indices were introduced: the Projected Axial Diffusivity (PAD) and the Pro-jected Radial Diffusivity (PRD). These parameters measure diffusion along refer-ence directions derived from a DT-dataset representative of the healthy brain, thus

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CHAPTER 3. PROJECTED DTI INDICES AS NEW MEASURES TO STUDY WM INTEGRITY

allowing a coherent comparison of diffusivity properties between subjects and in-dependent of focal brain lesions. To test this approach, Wheeler-Kingshott et al. conducted a pilot study on two MS patients, using the projected parameters to look for differences between each patient and a group of controls. The results suggested that the projected indices can give more information about MS pathology than the standard ones when the clinical condition is more severe.

The aim of this work is to develop a pipeline for comparative studies of MS patients and controls’ groups using this new approach and to test its feasibility for studying WM pathology. More specifically, this work will assess if the projected parameters, PAD and PRD, can depict different structural changes between con-trols and patients compared to their analogous standard parameters, AD and RD. In addition, differences in the orientation of DTs’ between healthy subjects and MS patients will be studied with the purpose of investigating if there are major differ-ences between the two groups due to MS pathology. Finally, the analysis’ results will be related to the areas of WM lesions detected by conventional MRI.

3.2 Methods

The methodology of this study can be divided into six main stages: • Processing pipeline;

• Registration;

• Calculation of DTI indices; • DTI indices statistical analysis; • Angle calculation and analysis;

• Creation of the Lesion Probability Map (LPM);

First, the DW-images were processed and used to calculate the DT-images. Subsequently, each DT-dataset was registered to a template created from a subset of healthy controls and MS patients.

Then, the standard anisotropic indices of diffusion, AD, RD and FA, and their correspondent projected parameters, PAD, PRD, Projected Fractional Anisotropy (PFA), were calculated. These measures were used to look for statistical significant differences between the group of controls and the group of MS patients. After that, the results of each pair of analogous parameters were compared.

In order to analyse the difference in the tensor’s orientation between the DT-datasets of controls and patients, the DT-DT-datasets of each group were averaged and then, for each voxel, the angle between the principal direction of each mean DT-dataset was calculated.

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Finally, a lesion probability map was created from standard T2-weighted scans to relate the study results to the MS patients’ areas of WM lesions that were detected by conventional MRI.

3.2.1 Data and processing pipeline

Subjects

The study population of this research was constituted by 124 subjects: 48 healthy controls and 76 MS patients. Twenty patients had a PP disease type, 27 were RR and 29 were SP. The demographics and clinical characteristics of the participants are described for the controls and for the different groups of patients in Table 3.1. The information regarding the clinical condition of the patients is given by the parameter Disease Duration (DD), which corresponds to the number of years that have passed since the patients were diagnosed; and by the EDSS score.

Table 3.1: Subject group descriptives (mean±standard deviation). Subject Age (years) Sex (M/F) Median EDSS (range) DD (years)

HC 41.7±13.0 24/24 - -MS patients 48.7±10.1 26/50 6 (1-8.5) 15.9±10.0 PP MS patients 51.3±10.1 7/13 6 (1.5-6.5) 12.9±7.72 RR MS patients 42.0±9.56 9/18 1.5 (1-6.5) 10.8±8.62 SP MS patients 53.2±7.19 10/19 6.5 (4.5-8.5) 22.8±8.69 Initial data

At the beginning of this project I was given a set of initial data for each subject, which is listed below:

• Eddy-corrected DW-data;

• Text files with unitary vectors representing the gradient directions and the corresponding b values of each acquisition;

• The transformations resultant from the eddy-current corrections.

Eddy currents are electric currents originated from the time-varying magnetic field that is formed during the DW-image acquisition. These currents generate resid-ual magnetic field gradients that, in turn, combine with the applied imaging gradient pulses. Consequently, the gradients experienced by the spins are not exactly the ones established for the acquisition, which causes distortions in the reconstructed DW-image. To minimize the artefacts caused by the distortions, eddy correction

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techniques are employed [30]. In this case, the DW-data was eddy-corrected using the FMRIB Software Library (FSL) (http://fsl.fmrib.ox.ac.uk/), which consists in a set of analysis tools for functional MRI, MRI and DTI brain imaging data.

For the patients, I was given further data in order to create the LPM: • T2-weighted MRI scans;

• Region of Interest (ROI) lesions masks drawn in the T2-weighted scans by an experienced neurologist of the group.

MRI Protocol

The MRI scans of the brain were acquired using a Philips Achieva 3T system (Philips Healthcare, Best, The Netherlands) with a 32-channel head-coil.

The DW-data was acquired with a diffusion-weighted spin-echo echo-planar imaging (DW-SE-EPI) sequence. In addition, the following parameters were used: Echo Time (TE) = 68 msec, Repetition Time (TR) = 24 sec with cardiac gating to limit physiological noise artefacts, 2x2x2 mm3voxel size, 61 isotropically distributed diffusion-weighted directions with b = 1200 s.mm−2 plus 7 non diffusion-weighted (b = 0) (B0) volumes.

The T2-weighted scans were acquired with a dual-echo sequence (1x1x3 mm3, TR = 3500 msec, TE = 19/85 msec).

DT estimation

For each voxel, the DW-data was used to reconstruct information about the diffu-sion orientation, fitting it to an ellipsoid. The DT estimation was done using the UCL Camino Diffusion MRI Toolkit (http://cmic.cs.ucl.ac.uk/camino), which is an open-source software toolkit for diffusion MRI processing.

Camino has a range of standard and advanced fitting algorithms. For this work, a linear diffusion tensor model was used, in which the elements of the diffusion tensor are calculated from a standard linear least-squares fit.

To perform the fitting, it was necessary to define a schemefile listing the de-tails of the acquisition of each DW-image. This was made using the information about the gradient directions and the b-values. However, before doing this step, the gradient vectors needed to be rotated according to the eddy-current correction transformations. This rotation was applied using FSL.

After the fitting, the DTs’ information was saved in a 5-dimensional image (dim1=112, dim2=112, dim3=72, dim4=1, dim5=6) with the first 3 dimensions representing the size (x,y,z) of the image, the 4th dimension indicating that there

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is no time axis, and the 5th dimension representing the 6 components of the tensor: Dxx, Dyx, Dyy, Dzx, Dzy, Dzz.

3.2.2 Registration

This work uses a Voxel-Based Analysis (VBA) to anatomically localize WM dif-ferences between the groups of controls and patients. Before conducting a VBA it is mandatory to spatial normalize all DT-images in order to remove the size and shape differences of the brains. After spatially normalization, correspondent voxels across the cohort should represent the same anatomical structures and any remain-ing differences between subjects should correspond to differences in their diffusion properties.

Choice of the registration method

Different methods for normalizing DT images have been proposed in the litera-ture. In the most simple procedures, the registration is performed using DTI scalar indices, such as FA, so that it is possible to use the traditional intensity-based reg-istration methods [31]. However, this scalar-based normalization method doesn’t consider the orientation information encoded in the DTs, which is of major impor-tance since each DT should be aligned according to the image’s underlying anatom-ical structure [7]. In order to maintain the DTs orientation consistent with the subject anatomy after image transformation, it is necessary to reorient the tensor fields according to the performed transformation. The importance of this procedure is illustrated in Figure 3.1.

One of the reorientation strategies commonly used to reorient the DT images is the Preservation of Principal Directions (PPD) algorithm [32]. It rotates the DT in a way consistent with the reorientation of the tissue caused by the registration. On the other hand, the size and shape of the tensor, i.e. its eigenvalues, are preserved, because they reflect the properties of the underlying tissue microstructure [32].

More complex registration methods use full tensor information. DTI-TK (http: //dti-tk.sourceforge.net) [34, 35] is a publicly available tool that performs spatial normalisation of DTI data. This registration algorithm matches tensors as a whole, which improves the alignment of diffusion tensor images compared to the scalar-based method.

Due to the enhanced performance in tensors alignment compared to other spatial normalization methods [36], DTI-TK was chosen to perform the registration in this work. Thus, using this toolkit, each DT-dataset was registered to a DT-image template.

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Figure 3.1: Importance of tensor reorientation after registration. A - In the original DT-image, the tensor field is aligned with the axonal fibre. B - After being warped with the scalar-based registration transformation, the tensors are no longer aligned with the underlying anatomy. C - However, reorienting the tensors after the scalar-based registration, realigns the ellipsoids with the fibre track. Image adapted from [33].

Preprocessing

Before using DTI-TK, it was required to perform a preprocessing step on the DT-data.

First, the non-brain tissues were removed from the images using the Brain Ex-traction Tool (BET) [37] of FSL, which is an automated method for separating the brain tissue from the non-brain tissue of MR head images.

This tool couldn’t be applied directly to the DT-datasets nor to the DW-images, due to their contrast. Instead, the 7 B0 images of each participant were averaged and then the resulting mean image was used with the BET tool. This tool has an option to choose a fractional intensity threshold that determines the edge of the brain outline. It ranges from 0 to 1 and its default value is 0.5. For this dataset, a value of 0.2 was chosen, which results in a larger estimated brain than the default. This value was chosen because it was the best at avoiding the removal of brain tissue and at minimizing the quantity of non-brain tissue kept. Finally, each DT-dataset was masked with its correspondent brain-extracted mean B0-image.

The next step was to ensure that the DT-datasets were SPD matrices. Although this condition is part of the definition of a tensor, in practice, during the DT estimation, the noise from the DW-images may cause this not to happen in some voxels. This usually occurs in the voxels around the boundary of the brain, due to an imperfect brain extraction, and in the voxels where there was an imperfect correction of motion or eddy-current distortions. Nonetheless, this condition is important to make sure that the DT-datasets behave correctly after successive processing steps. Using a tool in DTI-TK, it was possible to identify the non-SPD voxels and enforce this condition on them. In addition, by observing the images of the non-SPD voxels, it was possible to check that this condition was verified in very few voxels inside the brain, revealing that the DW-data was not markedly noisy.

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Template

Using a population-specific template, that is morphologically closer to the subjects in the cohort, can improve the accuracy of registration. Therefore, the template was created using a subset of the study population, constituted by 20 healthy controls and 20 MS patients.

The template was constructed from both patients and controls in order to mini-mize the transformations needed in the registration for each subject. If the template was based on a healthy population alone, it would imply stretching the MS brains to a larger degree than healthy brains when performing registration.

The subjects for the template were chosen so that the average characteristics (age, sex and EDSS) of the subset were representative of the entire cohort. The information regarding the MS course of the disease for each patient was only avail-able after the registration phase of the project. For this reason, the MS type is not as equally distributed between the patients’ group as it would have been desirable. A higher number of participants from the cohort was not included in the tem-plate because it would have demanded a longer computation time and this number of subjects was considered to be sufficient to create a representative template of the study population.

The characteristics of the individuals chosen for the template are shown in Table 3.2.

Table 3.2: Template group descriptives (mean±standard deviation)

HC MS Patients

Age(years) 51.3±10.1 46.9±13.0

Sex(M/F) 7/13 11/9

Median EDSS (range) - 4.25 (1-8.5)

DD(years) - 14.2±11.2

Type of MS (PP/RR/SP) - (3/9/8)

The template was built using DTI-TK [38], which has a pipeline specifically designed for constructing templates with DT-images. DTI-TK starts by bootstrap-ping an initial template and then optimizes it with affine and deformable alignments. The affine alignment uses linear transformations (rotation, translation, scale and shear) to change objects’ global size and shape whereas deformable alignment re-moves size or shape differences between local structures using affine and non-linear transformations.

First, the selected DT-images were rigidly aligned to an existing template, rec-ommended for the DTI-TK’s spatial normalization pipeline, named ”IXI aging

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tem-CHAPTER 3. PROJECTED DTI INDICES AS NEW MEASURES TO STUDY WM INTEGRITY

plate” [39]. Since the rigid alignment includes only rotational and translational transformations, the IXI aging template doesn’t have any influence on the size and shape of the constructed template. The purpose of this step is just to locate and orient the final template in space in a consistent way with the standard template spaces, such as the Montreal Neurological Institute (MNI) brain space.

After the rigid alignment, the initial template is computed as a log-Euclidean mean of the registered DT-images. Log-Euclidean operations are used instead of usual Euclidean operations, because the latter are problematic when working on tensors. However, these difficulties are avoided when tensors are transformed into their matrix logarithms [40].

In the next steps, the averaged template is iteratively improved. The DT-images are registered to the template and then a refined template is obtained as the average of the registered DT images for the next iteration. This procedure is repeated until the difference between templates from consecutive iterations becomes sufficiently small, first with affine and then with non-linear registrations [41].

The final template can be observed in Figure 3.2.

Figure 3.2: Template created. A - FA map (sagittal view). B – FA map (axial view). C - Ellipsoid representation with colour coding. Red corresponds to diffusion along the transverse axis; blue, to diffusion along the inferior-superior axis; and green, to diffusion along the anterior-posterior axis. The tensors in the genu and splenium (in red) of the corpus callosum should be aligned with the transverse axis, like in this image. This is a very important feature and allows checking if the tensors are correctly reconstructed.

Registration and image mapping

All the subjects were registered to the template using a pipeline involving rigid, affine and deformable alignment. For each subject, DTI-TK outputs two transfor-mations (affine and deformable) that together define the mapping from the subject native space to the template space.

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In order to minimize the smoothing effect of interpolation, it is desirable to warp the subject data to the template space with a single interpolation. Thus, it was necessary to use a DTI-TK command to combine the two transformations into one before applying it.

At the end of this stage, all DT-images shared a common space, allowing a voxel-based comparison between subjects.

3.2.3 Calculation of the DTI indices

Original indices

The eigenvectors and eigenvalues of each DT-dataset were extracted with DTI-TK and then, the maps for AD, RD and FA were calculated using their standard expressions with Matlab (http://www.mathworks.com/).

Projected indices

The projected parameters PAD, PRD and PFA were calculated by projecting the obtained tensors in the most likely healthy direction of diffusion. In order to define this healthy direction, the DT-datasets from the entire cohort of 48 controls were averaged in a DT-dataset of reference. Again, this was done using DTI-TK, which employs log-Euclidean metrics.

Then, for each voxel, the reference eigenvectors and their corresponding eigen-values were extracted from the DT-dataset of reference. The projected indices were calculated according to their usual expressions but using the projected eigenvalues instead of the original ones obtained directly from the DT. In this work, the wording ”projected eigenvalue” refers to the magnitude of the projection of all components of a DT in the direction of a certain reference eigenvector.

For each voxel of each subject n (with n = 1,...,124), the jthprojected eigenvalue λn,j,proj (with j = 1, 2 or 3) was calculated with Matlab according to the following

expression:

λn,j,proj = (vj,ref)T · DTn· (vi,ref) (3.1)

Where vj,ref corresponds to the jth reference eigenvector and DTn corresponds

to the diffusion tensor of that subject’s voxel.

A description of the projected indices calculation process is summarized in Fig-ure 3.3.

It is important to remark that, by definition, λ1,proj is never higher than the

corresponding λ1, and that λ2,proj and λ3,proj are never smaller than λ2 and λ3,

respectively. Consequently, whilst PAD is never higher than the corresponding AD, PRD is never smaller than the corresponding RD.

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Figure 3.3: Schematics of the projected indices calculation.

In the previous published work with projected indices [1], the index PFA hadn’t been considered. This parameter was included in this study because PFA informs about the anisotropy of the projected DT, which can be representative of changes in the alignment of the tensors.

3.2.4 DTI indices statistical analysis

The correspondent indices from controls and patients were statistically compared in order to identify the white matter areas with pathological abnormalities.

This analysis was conducted using the Statistical Parametrical Mapping (SPM) 8 software (http://www.fil.ion.ucl.ac.uk/spm/software/spm8/), which is used to identify regionally specific differences in the brain.

With this software, a VBA was performed to compare the indices AD, RD, FA, PAD, PRD, and PFA between controls and patients.

For each measure, the group of controls was compared with 6 different group combinations of MS patients:

• all 76 MS patients; • patients with PP MS; • patients with SP MS; • patients with RR MS;

• SP and RR patients with EDSS<6; • SP and RR patients with EDSS≥6.

For each analysis, a 2-sample t-test was used, with age and sex as covariates. In addition, to ensure that only the white matter was considered in the study, an

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analysis mask was defined from the FA map of the template thresholded for voxels with FA≥0.3.

The differences between patients and controls were deemed to be significant for a p-value<0.05, after correcting for the Familywise Error Rate (FWE) for multiple comparisons.

Before performing the statistical analysis, the images were smoothed with SPM8 [42] by being processed with a low pass filter derived from a Gaussian kernel with Full Width at Half Maximum (FWHM) of 8-mm. This step is very important for increasing the validity of the results: it makes the data more normally distributed, which is a property required by SPM; it improves the SNR; and it helps attenuating imperfections from the registration.

The width of the smoothing kernel was chosen based on the recommendations of a study that investigated the best filter size in DT-MRI data analysis [17] and by observing the results obtained with different filter sizes.

The output of each analysis is a statistical map showing regions where the brain differs significantly among the two groups.

3.2.5 Angles calculation and analysis

It was studied how the orientation of the tensors differed between the average of controls and the average of patients.

First, identically to the process of averaging the controls’ DT images, which resulted in the DT-dataset of reference, the mean of the MS patients’ DT-images was calculated.

Then, for each voxel, the angle separating the corresponding tensors of each mean DT-dataset was calculated using the definition of the dot product:

α = Arccos v1,ref • v1,ms |v1,ref||v1,ms| (3.2) Where v1,ref and v1,ms correspond, respectively, to the principal eigenvector of

the reference DT-dataset and to the principal eigenvector of the MS patients’ mean DT-dataset.

The angle α was calculated from the absolute value of the dot product because, although the two principal eigenvectors may form an angle greater than 90◦, the smaller angle between the two tensor principal axes never goes beyond that value.

Finally, the resulting volume was thresholded for voxels with FA≥0.3 and then the magnitudes of the angles were observed to investigate the areas with higher dispersion between the two averaged groups.

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3.2.6 Creation of the lesion probability map

To relate significant differences between patients and controls with the localization and extension of the lesions detected with standard MRI, it was necessary to create a LPM. This map represents the likelihood of finding a lesion in a certain voxel across a group of patients.

As previously mentioned, the LPM was created from T2 hyperintense MS lesion masks drawn by an experienced neurologist.

First, the lesion masks, originally in their individual space, needed to be mapped into the common space of the DT-template. However, since it is not possible to register the T2 images to the information in a tensor image, the B0 images were used as target instead.

Therefore, a mean B0 template was created. The mean B0 image of each patient was mapped onto the DT template space by applying the correspondent transforma-tion resultant from the initial DT-dataset registratransforma-tion. This was possible because for each subject, the original B0 scans and DT-datasets were in the same native space.

Subsequently, the B0 mean images in the template space were averaged, consti-tuting a mean B0 template. Then, each T2-weigthed MRI scan was registered to the B0 mean template using linear and non linear transformations from Nifty Reg (http://sourceforge.net/projects/niftyreg/). These transformations were combined into one single transformation, which was then applied to the lesion mask of the corresponding patient.

Figure 3.4: Lesion probability map created.

All registered lesion masks were binarized and then averaged. The resultant image is the final LPM, which is presented in Figure 3.4.

It can be observed that the cohort of patients had their lesions quite dispersed in the WM. In fact, the mean value of the LPM is 0.04, which correspond to the overlap of lesions in just 4% of the patients.

When relating the analysis’ results with the presence of lesions, the LPM was

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thresholded for values above 10%. Due to the dispersion of the lesions, it wouldn’t be advantageous to threshold the map at a higher value. Thereby, the thresholded LPM show regions where at least 10% of the patients present lesions.

3.3 Results

3.3.1 Statistical analysis

Comparison between patients and controls

In comparison with the normal controls, all groups of MS patients presented regions with significantly increased AD, PAD, RD and PRD and decreased FA and PFA. No significant differences were found for the opposite case (decrease of AD, PAD, RD and PRD and increase of FA and PFA).

The extension of the differences obtained between the controls and the vari-ous groups of MS greatly differed between them. Regarding the MS types groups (PP, SP and RR), the highest extent of significant patient-controls differences was observed for the SP and EDSS≥ 6 cohorts and the smallest for the PP group.

Additionally, it was observed that, for each measure, the results of the analysis between the controls and the whole group of MS patients were very similar to the ones obtained between the controls and the SP group and between the controls and the EDSS≥ 6 group. This is understandable since the median EDSS of the 76 patients group is 6 and the median EDSS of the SP group is 6.5.

Figure 3.5: Results showing areas with increased PAD (blue) in MS patients comparing to controls. Pink represents the LPM thresholded at 10%.

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The results obtained for an increase in PAD and PRD and a decrease in PFA, between the controls and the entire group of patients, can be found, respectively, in Figures 3.5, 3.6 and 3.7.

Figure 3.6: Results showing areas with increased PRD (blue) in MS patients comparing to controls. Pink represents the LPM thresholded at 10%.

Figure 3.7: Results showing areas with decreased PFA (blue) in MS patients comparing to controls. Pink represents the LPM thresholded at 10%.

In general, the increase of RD and PRD was found in more areas than the changes in the rest of the measures. Nonetheless, there are a lot of regions where the changes between the indices PRD, PAD and PFA (Figures 3.5-3.7) and between the indices AD, RD and FA overlap with each other.

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Additionally, it was common to find regions where areas of indices’ changes overlapped with the LPM thresholded at 10%. These changes usually extended to regions outside the lesions. However, there were also regions where the thresholded LPM was not accompanied by significant changes in the parameters.

Original and projected indices

The purpose of this analysis was to investigate whether the projected indices (PAD, PRD and PFA) would present higher sensitivity to white matter changes caused by MS pathology than the standard indices (AD, RD and FA).

Figure 3.8: Comparison between the projected and original indices, considering all MS patients. Blue and pink represent areas with changes in the MS patients detected, respec-tively, with the standard and the projected parameters. In addition, purple corresponds to the overlay between the blue and the pink areas and the olive green represents the LPM thresholded at 10%.

The results showed that changes detected with the projected parameters mostly overlapped with the ones detected with the standard parameters, with exception to

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some voxels or small areas (Figure 3.8).

This observation was common to the results between the controls and all the different MS groups. For this reason, the only differences between the projected and original indices that are reported in this work belong to the analysis between the two entire cohorts.

In general, the areas with increase of PAD were less extensive than the areas with increased AD. Conversely, the areas with increase of PRD and decrease of PFA were more extensive than the areas with increase of RD and decrease of FA, respectively. Nonetheless, the maps of changes in RD and PRD were the ones showing less differences between the two.

Differences between the projected and original parameters were more frequently found in the superior part of the brain. In addition, some small regions where a decrease in PFA occurred as a result of an increase in PRD were observed. However, the analogous didn’t happen regarding changes in the standard parameters (Figure 3.8 slices 52 and 54).

Since the changes in the two types of parameters were very similar, it is difficult to relate their differences with the thresholded LPM. Nonetheless, in Figure 3.8, in slices 50 and 53 from the first row, there are some voxels where an increase of AD coincides with the thresholded LPM or is in the surrounding area and there are no significant changes in PAD. On the other hand, in slice 52 from the second row and in slice 52 from the third row, the thresholded LPM seems to extend from the original measures RD and FA to the projected PRD and PFA, respectively.

3.3.2 Angles analysis

In this analysis, the angle between corresponding DTs of controls and patients’ averages was measured for the WM.

Most voxels from the angle map showed very small differences between the orientation of corresponding mean DTs (Figure 3.9). The deviation between the two varied mostly between 0 and 5 degrees, although, in some voxels or in certain small areas, this difference increased. In fact, there were some well defined regions where the angles varied from 10 to 20 degrees.

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Figure 3.9: Results of the angle dispersion analysis between the mean DT-datasets: values of the angles between the corresponding tensors of the mean MS patients DT-dataset and the mean HCs DT-DT-dataset.

3.4 Discussion

In this work, brain white matter changes in MS were investigated by standard diffusion indices (AD, RD and FA) and by projected diffusion indices (PAD, PRD and PFA) with the purpose of validating the latter as a more consistent approach to study white matter integrity in diseased brains.

The analysis started by comparing the HCs with different MS groups in order to assess if the differences between the standard and projected measures would vary according with the clinical characteristics of the patients. However, the differences in the patients-controls changes detected by the projected and by standard param-eters were similar for all the different comparisons: the changes detected by the two different approaches mostly overlapped. Therefore, this study focused only on analysing the results between the statistical comparison of controls and the entire cohort of patients.

The WM abnormalities detected with the standard and projected indices were compared, so that it was possible to conclude whether this new approach could

Methodological study on diffusion tensor indices in MS: analysis challenges and outcomes

Methodological Study on Diffusion Tensor

Indices in MS: Analysis Challenges and

Outcomes

Catarina Correia de Freitas

Methodological Study on Diffusion Tensor

Indices in MS: Analysis Challenges and

Outcomes

Catarina Correia de Freitas

Contents

List of Figures

List of Tables

List of Abbreviations

Chapter 1

Introduction

1.1

Aim of the work

1.2

Dissertation outline

Chapter 2

Background

2.1

Measuring diffusion in the brain

2.2

Diffusion tensor imaging

2.3

Multiple sclerosis and DTI

Chapter 3

Projected DTI indices as new

measures to study WM integrity

3.1

Motivation and objectives

3.2

Methods

3.2.1

Data and processing pipeline

3.2.2

Registration

3.2.3

Calculation of the DTI indices

3.2.4

DTI indices statistical analysis

3.2.5

Angles calculation and analysis

3.2.6

Creation of the lesion probability map

3.3

Results

3.3.1

Statistical analysis

3.3.2

Angles analysis

3.4

Discussion